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A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their group Automorphisms.
References
Klein, F. ``Vergleichende Betrachtungen über neuere geometrische Forschungen.'' 1872.
Yaglom, I. M. Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century.
Boston, MA: Birkhäuser, 1988.